Predicting User Collections
Phil Henrickson
2023-06-28
What is this?
This notebook contains a set of analyses for analyzing mrbananagrabber’s BoardGameGeek collection. The bulk of the analysis is focused on building a user-specific predictive model to predict the games that the specified user is likely to add to their collection.
By analyzing a user’s collection and training a predictive model, I am able to answer questions such as:
What designers/mechanics/genres does a user tend to like or dislike?
What older games might they be interested in adding to their collection?
What new and upcoming games should they check out?
1 Data
1.1 Outcomes
How many games has mrbananagrabber owned/rated/played?
1.2 Collection
What types of game does mrbananagrabber own? I can look at the most frequent types of categories, mechanics, designers, and artists that appear in a user’s collection.
1.3 Collection Table
What games does mrbananagrabber currently have in their collection? The following table can be used to examine games the user owns, along with some helpful information for selecting the right game for a game night!
Use the filters above the table to sort/filter based on information about the game, such as year published, recommended player counts, or playing time.
2 Modeling
I’ll now the examine predictive models trained on the user’s collection.
For an individual user, I train a predictive model on their collection in order to predict whether a user owns a game. The outcome, in this case, is binary: does the user have a game listed in their collection or not? This is the setting for training a classification model, where the model aims to learn the probability that a user will add a game to their collection based on its observable features.
How does a model learn what a user is likely to own? The training process is a matter of examining historical games and finding patterns that exist between game features (designers, mechanics, playing time, etc) and games in the user’s collection.
Note: I train models to predict whether a user owns a game based only on information that could be observed about the game at its release: playing time, player count, mechanics, categories, genres, and selected designers, artists, and publishers. I do not make use of BGG community information, such as its average rating or number of user ratings (though I do use a game’s estimated complexity as a feature). This is to ensure the model can predict newly released games and is not dependent on the BGG community to rate them.
2.1 What Predicts a User’s Collection?
A predictive model gives us more than just predictions. We can also ask, what did the model learn from the data? What predicts the outcome? In the case of predicting a boardgame collection, what did the model find to be predictive of games a user owns?
To answer this, I can examine the coefficients from a model logistic regression with ridge regularization (which I will refer to as a penalized logistic regression). Positive values indicate that a feature increases a user’s probability of owning/rating a game, while negative values indicate a feature decreases the probability. To be precise, the coefficients indicate the effect of a particular feature on the log-odds of a user owning a game.
This model examines a wide variety of features of games (505 features, to be exact) and estimates their effect on whether a user owns a game. These estimates are then shrunken towards zero based on a tuning parameter (lambda), where the appropriate value is estimated from the data.
The following visualization shows the path of each feature as it enters the model, with highly influential features tending to enter the model early with large positive or negative effects.
2.2 Partial Effects
This type of model enables me to I can examine the effects of specific features on a user’s collection. For instance, what is a user’s favorite designer? Least favorite mechanic? The following plots indicate specific effects for different kinds of features.
2.3 Feature Importance
In addition to training a logistic regression, I trained another type of model using boosted trees (LightGBM), a flexible nonparametric method that is well suited for prediction.
Which features were most used by this model? Features that are important in predicting a user’s collection will appear towards the top of cover, frequency, and/or gain.
3 Assessment
How well did the model do in predicting the user’s collection?
This section contains a variety of visualizations and metrics for assessing the performance of the model(s). If you’re not particularly interested in predictive modeling, skip down further to the predictions from the model.
3.1 Separation
An easy way to examine the performance of classification model is to view a separation plot.
I plot the predicted probabilities from the model for every game (from resampling) from lowest to highest. We then overlay a blue line for any game that the user does own. A good classifier is one that is able to separate the blue (games owned by the user) from the white (games not owned by the user), with most of the blue occurring at the highest probabilities (right side of the chart).
I can more formally assess how well each model did in resampling by looking at the area under the receiver operating characteristic curve (roc_auc). A perfect model would receive a score of 1, while a model that cannot predict the outcome will default to a score of 0.5. The extent to which something is a good score depends on the setting, but generally anything in the .8 to .9 range is very good while the .7 to .8 range is perfectly acceptable.
| type | wflow_id | .metric | mean | std_err | n |
|---|---|---|---|---|---|
| resamples | glmnet | roc_auc | 0.934 | 0.004 | 5 |
| resamples | lightgbm | roc_auc | 0.918 | 0.009 | 5 |
3.2 Top Games in Training
| Top (Older) Games for mrbananagrabber | |||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||
| rank | image | game | description | Pr(Own) | Own |
|---|---|---|---|---|---|
| 1 |  |
Unmatched: Little Red Riding Hood vs. Beowulf (2020) | In battle, there are no equals. ONCE UPON A TIME, Little Red Riding Hood took her basket of nasty tricks and faced off against the legendary Beowulf in this exciting Unmatched set. "What big eyes you have, Wulfie!" "That’s called 'rage', kid!" Little Red features a clever card-combo mechanism. Matching icons on the cards she plays to the one in her "basket" (discard pile), triggers potent e... | 0.946 | no |
| 2 |  |
Star Wars: Outer Rim (2019) | Take to the stars and become a living legend in Star Wars: Outer Rim, a game of bounty hunters, mercenaries, and smugglers for 1-4 players! In Outer Rim, you take on the role of an underworld denizen, setting out to make your mark on the galaxy. You'll travel the outer rim in your personal ship, hire legendary Star Wars characters to join your crew, and try to become the most famous (or infamo... | 0.945 | no |
| 3 |  |
Star Wars: Rebellion (2016) | Star Wars: Rebellion is a board game of epic conflict between the Galactic Empire and Rebel Alliance for two to four players. Experience the Galactic Civil War like never before. In Rebellion, you control the entire Galactic Empire or the fledgling Rebel Alliance. You must command starships, account for troop movements, and rally systems to your cause. Given the differences between the Empire ... | 0.941 | no |
| 4 |  |
Arkham Horror: The Card Game (Revised Edition) (2021) | The boundaries between worlds have drawn perilously thin. Dark forces work in the shadows and call upon unspeakable horrors, strange happenings are discovered all throughout the city of Arkham, Massachusetts, and behind it all an Ancient One manipulates everything from beyond the veil. It is time to revisit that which started it all… With a revamped system of organization and a number of quali... | 0.911 | no |
| 5 |  |
Orléans (2014) | During the medieval goings-on around Orléans, you must assemble a following of farmers, merchants, knights, monks, etc. to gain supremacy through trade, construction and science in medieval France. In Orléans, you will recruit followers and put them to work to make use of their abilities. Farmers and Boatmen supply you with money and goods; Knights expand your scope of action and secure your m... | 0.896 | no |
| 6 |  |
Unmatched: Battle of Legends, Volume Two (2021) | In battle, there are no equals. Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Batt... | 0.893 | yes |
| 7 |  |
Scythe (2016) | It is a time of unrest in 1920s Europa. The ashes from the first great war still darken the snow. The capitalistic city-state known simply as “The Factory”, which fueled the war with heavily armored mechs, has closed its doors, drawing the attention of several nearby countries. Scythe is an engine-building game set in an alternate-history 1920s period. It is a time of farming and war, broken h... | 0.874 | no |
| 8 |  |
Twilight Imperium: Fourth Edition (2017) | Twilight Imperium (Fourth Edition) is a game of galactic conquest in which three to six players take on the role of one of seventeen factions vying for galactic domination through military might, political maneuvering, and economic bargaining. Every faction offers a completely different play experience, from the wormhole-hopping Ghosts of Creuss to the Emirates of Hacan, masters of trade and ec... | 0.873 | yes |
| 9 |  |
Android: Netrunner (2012) | Welcome to New Angeles, home of the Beanstalk. From our branch offices in this monument of human achievement, NBN proudly broadcasts all your favorite media programming. We offer fully comprehensive streaming in music and threedee, news and sitcoms, classic movies and sensies. We cover it all. Ours is a brave new age, and as humanity hurtles into space and the future with an astonishing series ... | 0.866 | no |
| 10 |  |
Gaia Project (2017) | Gaia Project is a new game in the line of Terra Mystica. As in the original Terra Mystica, fourteen different factions live on seven different kinds of planets, and each faction is bound to their own home planets, so to develop and grow, they must terraform neighboring planets into their home environments in competition with the other groups. In addition, Gaia planets can be used by all faction... | 0.862 | no |
Top 10 games most likely to be owned by the user in the last 10 years of the training set, highlighting in blue games that are currently in the user’s collection and light blue for games that the user previously owned.
| Top Games by Year for mrbananagrabber | |||||||||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||||||||
| Rank | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | A Few Acres of Snow | Android: Netrunner | Lewis & Clark: The Expedition | Orléans | Star Wars: Armada | Star Wars: Rebellion | Twilight Imperium: Fourth Edition | Star Wars: Legion | Star Wars: Outer Rim | Unmatched: Little Red Riding Hood vs. Beowulf | Arkham Horror: The Card Game (Revised Edition) |
| 2 | Takenoko | Merchant of Venus (Second Edition) | BANG! The Dice Game | Hyperborea | DRCongo | Scythe | Gaia Project | Star Wars: X-Wing (Second Edition) | KeyForge: Age of Ascension | Gloomhaven: Jaws of the Lion | Unmatched: Battle of Legends, Volume Two |
| 3 | Eclipse | The Great Zimbabwe | Rococo | AquaSphere | Unusual Suspects | Mansions of Madness: Second Edition | Sherlock Holmes Consulting Detective: Carlton House & Queen's Park | Don't Get Got! | Unmatched: Robin Hood vs. Bigfoot | Unmatched: Buffy the Vampire Slayer | Don't Get Got!: Shut Up & Sit Down Special Edition |
| 4 | Hawaii | Kemet | World of Tanks: Rush | Deus | Blood Rage | Pandemic: Reign of Cthulhu | Dinosaur Island | Cosmic Encounter: 42nd Anniversary Edition | Paris: La Cité de la Lumière | Dune: Imperium | Gravwell: 2nd Edition |
| 5 | The Adventurers: The Pyramid of Horus | Archipelago | Glass Road | Star Wars: Empire vs. Rebellion | Mombasa | Avenue | Heaven & Ale | Rising Sun | Century: Golem Edition – Eastern Mountains | Unmatched: Jurassic Park – InGen vs Raptors | Newton & Great Discoveries |
| 6 | A Game of Thrones: The Board Game (Second Edition) | Serenissima (Second Edition) | A Study in Emerald | Linko! | Karuba | Dead of Winter: The Long Night | Unlock!: Escape Adventures | Concordia Venus | Unmatched: Battle of Legends, Volume One | Hallertau | Great Western Trail (Second Edition) |
| 7 | Mage Knight Board Game | Terra Mystica | Terror in Meeple City | Fields of Arle | T.I.M.E Stories | One Night Ultimate Vampire | Spirit Island | Lords of Hellas | The Lord of the Rings: Journeys in Middle-Earth | Cosmic Encounter Duel | Sword & Sorcery: Ancient Chronicles |
| 8 | The Lord of the Rings: The Card Game | Star Wars: The Card Game | Gearworld: The Borderlands | The Werewolves of Miller's Hollow: The Pact | Risk: Europe | Hit Z Road | Sagrada | Crown of Emara | Era: Medieval Age | Unmatched: Cobble & Fog | Cascadia |
| 9 | Dust Tactics: Revised Core Set | Descent: Journeys in the Dark (Second Edition) | Spyrium | Akrotiri | The Grizzled | Star Wars: Destiny | Iberian Gauge | Brass: Birmingham | Aftermath | Hunt A Killer: Death at the Dive Bar | Unfathomable |
| 10 | Tragedy Looper | Polis: Fight for the Hegemony | The Ravens of Thri Sahashri | Pandemic: Contagion | The Bloody Inn | Pandemic: Iberia | Star Wars: Destiny – Two-Player Game | Vengeance | Tapestry | Pandemic Legacy: Season 0 | Explorers |
3.3 Calibration
What do the model’s predicted probabilties mean? Or, put another way, how well calibrated are the model’s predictions?
If the model assigns a probability of 5%, how often does the outcome actually occur? A well calibrated model is one in which the predicted probabilities reflect the probabilities we would observe in the actual data. We can assess the calibration of a model by grouping its predictions into bins and assessing how often we observe the outcome versus how often each model expects to observe the outcome.
A model that is well calibrated will closely follow the dashed line - its expected probabilities match that of the observed probabilities. A model that consistently underestimates the probability of the event will be over this dashed line, be a while a model that overestimates the probability will be under the dashed line.
3.4 Validation
I first assessed the models based on their performance via resampling on the training set.
But how well does my modeling approach do in predicting new games? To test this, I assessed the performance of the model (which was trained on games published through 2021) on games published in 2022-2023.
How well did the model do? The following table shows the model’s predictions for games in the validation set.
As before, I can then assess the performance of the model.
| type | wflow_id | .metric | .estimate |
|---|---|---|---|
| valid | glmnet | mn_log_loss | 0.012 |
| valid | lightgbm | mn_log_loss | 0.009 |
| valid | glmnet | roc_auc | 0.927 |
| valid | lightgbm | roc_auc | 0.964 |
4 Predictions
What new and upcoming games does the model predict for mrbananagrabber?
The following table displays the top 15 games published after 2021 with the highest probability of entering the user’s collection.
| Top 15 (Newer) Games for mrbananagrabber | |||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||
| rank | image | game | description | Pr(Own) | Own |
|---|---|---|---|---|---|
| 1 |  |
Gloomhaven: Second Edition (2024) | Gloomhaven: Second Edition is a revised and elevated version of the award-winning core game of Gloomhaven. This is the culmination of everything Isaac Childres and the growing Cephalofair Games team have learned since the initial release of Gloomhaven, including feedback from the community, playtesters, co-designers, and developers. The world, story, and challenging gameplay are all still the ... | 0.837 | no |
| 2 |  |
Terminus (2023) | You and your competitors’ transit companies have been hired by the city to build new subway lines and commercial developments to improve the city's bottom line. Manage assets such as time, money, & resources to build your subway line. Gain prestige by completing objectives and fulfilling the city’s transit demands. Focus on individual projects, open Agendas or a little of both in an effort t... | 0.816 | no |
| 3 |  |
The Witcher: Old World (2023) | In The Witcher: Old World, you become a witcher — a professional monster slayer — and immerse yourself in the legendary universe of The Witcher franchise. Set years before the saga of Geralt of Rivia, The Witcher: Old World explores a time when monsters roamed the Continent in greater numbers, creating a constant peril that required the attention of expertly trained monster slayers, known as w... | 0.709 | no |
| 4 |  |
Star Wars: The Deckbuilding Game (2023) | The Rebel Alliance fights valiantly against the tyranny of the Galactic Empire. Each new victory brings the Rebels hope, and each heroic sacrifice strengthens their resolve. Still, the Empire's resources are vast, and the firepower of its Empire Navy is unmatched. With neither side willing to accept defeat, their war rages across the galaxy... In Star Wars: The Deckbuilding Game, a head-to-hea... | 0.659 | no |
| 5 |  |
Unmatched: Jurassic Park – Dr. Sattler vs. T. Rex (2022) | In battle, there are no equals. "Dinosaurs eat man… Woman inherits the earth." The greatest predator the world has ever known is closing in on the tenacious Dr. Sattler. Who has the slightest idea what to expect? In Unmatched: Jurassic Park – Dr. Sattler vs. T. Rex, the massive T rex unleashes fearsome attacks and seems unstoppable while Dr. Sattler makes full use of her surroundings and the a... | 0.617 | yes |
| 6 |  |
Ticket to Ride Legacy: Legends of the West (2023) | In Ticket to Ride Legacy: Legends of the West, players embark on twelve journeys across North America as 19th century pioneers. The campaign begins on the East Coast, with players working their way to the West from one adventure to the next, meeting challenges along the way. As in Ticket to Ride, completing your tickets will remain your primary goal, but you will need to develop other skills if... | 0.552 | no |
| 7 |  |
Galactic Cruise (2024) | Hello, and welcome to Galactic Cruise. Here, we offer our guests something special: the comfort of a luxury cruise with the innovation of space travel. As the first company to offer extended-stay space vacations, we are excited to have you working for us! As a supervisor of this company, you’ll be expected to not only build these shuttles and satisfy our guests, but also to help the company th... | 0.397 | no |
| 8 |  |
Unmatched: Teen Spirit (2023) | Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Unmatched: Teen Spirit features four ... | 0.325 | no |
| 9 |  |
Tycoon: India 1981 (2023) | Post independence from colonial rule, India had been left in shambles. It was the combined efforts of bureaucrats, politicians, and industrialists who worked together (and sometimes not so much together) to start a new industrial revolution following the five-year plans. It is the dawn of a new era, for liberalization and globalization has removed much of the licensing and red-taping that had h... | 0.315 | no |
| 10 |  |
Undaunted: Battle of Britain (2023) | The RAF faces the Luftwaffe in this two-player deck-building game of aerial WWII combat. Summer, 1940. The German war machine has rolled through the continent in less than a year, crushing all before it. Britain is all that stands in the way of German victory in Europe. Command the pilots of the battle-tested Luftwaffe who are looking to extinguish all resistance and pave the way to invasion, ... | 0.307 | no |
| 11 |  |
Frosthaven (2022) | Frosthaven is the story of a small outpost far to the north of the capital city of White Oak, an outpost barely surviving the harsh weather as well as invasions from forces both known and unknown. There, a group of mercenaries at the end of their rope will help bring back this settlement from the edge of destruction. Not only will they have to deal with the harsh elements, but there are other, ... | 0.301 | yes |
| 12 |  |
Unmatched: For King and Country (2023) | Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Unmatched: For King and Country featu... | 0.258 | no |
| 13 |  |
Freaky Frogs From Outaspace (2023) | Finally you have time again for a pinball session. Let’s see how long you can keep the ball running on your favourite old pinball machine this time. If everything runs perfectly, you will start the nerve-wracking Multiball, or you gain an Extra Ball to play an additional round. Can you achieve a new High Score, or do you lose the balls faster than you are able to push the flippers? Freaky Fr... | 0.251 | no |
| 14 |  |
Cartagena: Escape Diaries (2023) | Cartagena: Escape Diaries is based on the classic game Cartagena and features multiple ways to play. In the original game, now dubbed the "First Escape", each player has a group of six animal pirates, and you want to be the first to have all six escape through the tortuous underground passage that connects the fortress to the port, where a sloop is waiting for them. To move a pirate, you need... | 0.240 | no |
| 15 |  |
Union Stockyards (2023) | Union Stockyards is a mid-weight economic euro game with unique features: A supply/demand driven market that is central to game play, not a sidebar. Low randomness -- market changes due to player decisions. A worker-placement game where your workers may go on strike. Extensively-researched historical theme about one of the great industrial wonders of U.S. Gilded Age. Ope... | 0.228 | no |
4.1 Explaining Individual Predictions
Why did the model predict these games?
4.2 Upcoming Games
Finally, I can examine predictions for all newer and upcoming games.